Mass modelling of dwarf spheroidals. Jorge Peñarrubia

Transcription

1 Mass modelling of dwarf spheroidals Jorge Peñarrubia Santiago de Chile 13 April 2015

2 Universe Composition Assumption: GR is correct WMAP7

3 DM particle models: Constraints 63 orders 51 orders

4 DM particle models: Constraints 63 orders CDM N-body collision-less simulations 51 orders

5 Constraints on DM-particle mass & cross-section 1- Counting number of structures in the Universe 2- Measuring inner structure of DM haloes 3- Seeking DM-annihilation signals in galaxies 4- Detecting DM particles on Earth 5- Manufacturing DM in particle accelerators

6 Substructure abundance

7 Substructure abundance λfs λfs average distance travelled by a DM particle before it falls in a potential well COLD ev WARM ev HOT <10 2 ev λfs ~ 3.7 pc (100 Gev / m ν ) 1/2 λfs ~ 100 kpc (1 kev / m ν ) λfs ~ 20 Mpc (30 ev / m ν )

8 The inner structure of DM haloes CDM haloes follow a centrallydivergent density profile dark matter cusp Dubinsky & Carlberg 91, NFW97, Moore+98, Diemand+ 05)

9 The inner structure of DM haloes Relic thermal energy (low particle mass) Scattering (large cross section) dark matter cores

10 The inner structure of DM haloes Relic thermal energy (low particle mass) Scattering (large cross section) dark matter cores

11 The extreme properties of dsphs Faintest galaxies in the known Universe: 10 3 < L/L sol < 10 7 Smallest 30 < r half /pc < 2000 Most numerous satellites Old, metal poor stellar populations 0.1 < age/gyr < 12 High mass-to-light ratios: 10 < M/L <1000 (Potential dominated by DM) DM particle mass & cross section Gravity tests Star formation/feedback in low mass haloes Hierarchical galaxy formation No gas No rotation

12 Text Illingworth (1976) mass estimate for Globular Clusters M = 167rc µ < vr2 > ( µ 4 King models) from 3 carbon stars: Walker+09 M/L = 0.72 < vr2 /(km/s)2 > 31 Hidalgo+13 Assumptions: Equilibrium mass follows light spherical shape isotropic velocity

13 Simon & Geha (2007) The era of multi-fibre spectrographs Assumptions: Equilibrium mass follows light spherical shape isotropic velocity Kleyna+02: 165 members Walker+09 Hidalgo+13

14 Simon & Geha (2007) The era of multi-fibre spectrographs Assumptions: Equilibrium mass follows light spherical shape isotropic velocity known form of the (DM) potential constant anisotropy Kleyna+02: 165 members Wilkinson+02: stars mass-loss tracers of the underlying potential = (1 + 0 r2 ) /2 } 0? = 2 ]5/2 [1 + (r/r ) c Walker+09 f(e,l) Anisotropic DF Wilkinson+02

15 Simon & Geha (2007) Schwarzschild modelling: orbits Assumptions: Equilibrium mass follows light spherical shape isotropic velocity known form of the (DM) potential arbitrary anisotropy Walker 12 Construction of orbital libraries in a given potential. Subset chosen in order to match v_los(r) DM = 0 (r/r s ) (1 + r/r s ) (3+ ) Using mock data Breddels+13 conclude that current current kinematic samples are too small to break degeneracies in the (spherical) halo profile Walker+09 Breddles+13

16 Simon & Geha (2007) Jeans modelling: fast and easy Assumptions: Equilibrium mass follows light spherical shape isotropic velocity known form of the (DM) potential arbitrary anisotropy Working with the moments of a DF is considerably simpler than constructing DF for a potential/luminous ( + 2 r ( r)= r(r) = r 2 1 (r) Z 1 r dr 0 r 02 (r spherical Jeans eqs. Walker+09 2 los(r) = 2 (R) Z +1 R dr 1 (r) R2 (r) 2 r r p r 2 r 2 R. 2

17 Simon & Geha (2007) Jeans modelling: fast and easy Assumptions: Equilibrium mass follows light spherical shape isotropic velocity known form of the (DM) potential arbitrary anisotropy Unknown β(r) Unknown M(r) (although fitting kurtosis(r) may help to break degeneracy, Richardson+Fairbairn 13,14) Walker 12 Working with the moments of a DF is considerably simpler than constructing DF for a potential/luminous 2 2 ( r ) + + ( r2 ) = 0. spherical r Z dr r (r ). r (r) = 2 r (r) 2 los (R) = (R) Walker+09 2 Z +1 dr 1 R 2 R (r) 2 r (r) r2 r p. r 2 R2 mass-anisotropy degeneracy Wilkinson+02

18 Breaking the degeneracy Walker & Peñarrubia (2011) M -- β degeneracy breaks at R Rhalf Peñarrubia+08; Walker+09; Wolf+10; Amorisco & Evans 2010 Wolf+10 M(R half ) µr half V 2 µ 480M pc 1 km 2 s 2 (Walker+09) mass estimator insensitive to β!!

19 Breaking the degeneracy Walker & Peñarrubia (2011) M -- β degeneracy breaks at R Rhalf Peñarrubia+08; Walker+09; Wolf+10; Amorisco & Evans 2010 Sculptor dsph Some dsphs show spatially + kinematically distinct stellar components Wolf+10 M(R half ) µr half V 2 µ 480M pc 1 km 2 s 2 (Walker+09) mass estimator insensitive to β!! Tolstoy + 04 (see also Battaglia+08)

20 Multi-component splitting Walker & Peñarrubia (2011) log M log R

21 Multi-component splitting Walker & Peñarrubia (2011) log M log R

22 Multi-component splitting Walker & Peñarrubia (2011) M R log M log R M(R h ) µr h h 2 i =1+ log[h 2 2i/h 2 1i] log[r h,2 /R h,1 ] directly from observables w/o dynamical modelling!

23 Sculptor, Fornax Walker & Peñarrubia (2011) NFW DM cusps ruled out in Sculptor and Fornax at a 93% and 97% confidence level apple 3 see also Amorisco & Evans(2012); Agnello & Evans(2012); Jardel & Gebhardt (2012)

24 Sculptor, Fornax... & Draco Walker, Peñarrubia, Mateo & Olzweski + 15 Preliminary With L~10 5 Lsol Draco is ~300 times fainter than Fornax and 50 times fainter than Sculptor

25 DM profile in fainter dsphs? Star formation histories (HST data) L<10 5 Lsol 10 5 Lsol 10 6 Lsol 10 7 Lsol Weisz+14 Faint dsphs only have one star formation episode multiple chemo-dynamical components??

26 Tidal streams of dsphs Errani, Peñarrubia & Tormen (2015) * Dark Matter 0 = (r/a) (1 + r/a) 3 =1 =0 cusp core * Stars (particle tagging)? = 0,? [1 + (r/r c ) 2 ] 5/2 N = 2x10 6 particles grid size = 10 pc Initial conditions chosen such that observables independent of halo profile M core (<r h )=M cusp (<r h ) M core M cusp =1+ a r h > 1 Cored models more massive!

27 Stellar streams: surface density

28 Tidal evolution of dsphs dsphs acted on by tides follow well-defined tidal tracks For same amount of mass lost cored dsphs are larger and colder than cuspy dsphs The sensitivity to core/cusp increases for deeply segregated stellar components (r*<<a)

29 Stellar streams: kinematics

30 Stellar streams: radial dependence normalized width and velocity dispersion of the stream to the half-light radius and mean velocity dispersion of the progenitor: cored dsphs lead to systematically hotter streams

31 streams: core/cusp problem PROGENITOR Systematic offset in stream properties at t=0 apple 1/2 GM(< rt ) z r t r t M 1/3 (e.g. Amorisco 2015) * fixing the progenitor s properties yields an offset in the associated stream! * offset increases with stream age & stellar segregation r t,core /r t,cusp ' 1.7 z,core/ z,cusp ' 1.7 * offset evolves parallel to tidal tracks

32 Summary Equilibrium models suggest that presence of DM cores extends down to L~10 5 Lsol dsphs embedded in cored haloes have streams that are systematically hotter than those embedded in cuspy haloes Depending on the age of the stream, the velocity dispersion of cored models can be 2-4x higher than those of cuspy models Difference increases with stream age and stellar segregation within the progenitor s DM halo Sgr is the obvious target in the MW Such (large) kinematic differences can be straightforwardly measured in streams associated to dsphs in external galaxies animations at: